In many image-processing applications it is desirable to apply both smoothing and sharpening to image data in order to improve their appearance. In the linear-filtering domain, smoothing is done by attenuating high-frequency components of the image (low-pass filtering). Alternatively, sharpening is done by amplifying high-frequency components, also known as Unsharp Masking (USM), which is expressed mathematically as:                               y          =                      x            +                          λ              ⁡                              (                                  H                  *                  x                                )                                                    ,                  (                      H            =                          I              -              L                                )                                    (                  Eq          .                                          ⁢          1                )            where x is the input image signal, y is the output image signal, λ is a real constant termed “the sharpness gain”, and H is a linear high-pass filter. The linear high-pass filter H can also be expressed as the difference between an identity-filter I and a linear low-pass filter L. The main advantage of linear filters for denoising or sharpening is their simplicity and efficiency. Unfortunately, sharpening and denoising undo each other's operation, so that achieving both effective denoising and effective sharpening is not possible with linear-filters. This remains true even when the denoising and sharpening are performed in separate steps.
Many selective denoising techniques have been investigated, which effectively attenuate selected types of noise without smoothing edges. These techniques do not utilize the selectiveness of the denoising filter to enhance edges and instead just leaved them un-smoothed. In a similar manner, many selective sharpening methods are known which effectively enhance edges without attenuating small amplitude noise in flat regions. These techniques do not utilize the selectiveness of the sharpening filter to denoise non-edge regions and instead just leave them unsharpened.
There are also many image-enhancement techniques that are known, which perform both denoising and sharpening. Most are based on a hard classification of neighborhoods corresponding to “non-features” (e.g., background, noise), and “features” (edges). Then a denoising algorithm is applied to “non-feature” neighborhoods and an unrelated sharpening algorithm is applied to “feature” neighborhoods. One limitation of such an approach is its relatively high computational complexity. Specifically, there are two separate operations that are performed at each pixel: a block/neighborhood classification and either a smoothing or a sharpening operation. Another limitation of the “hard” classification approach is the possibility of artifacts due to misclassifications, especially in noisy images.
This drawback can be eliminated, in part, by performing another technique in which both a smoothing operation and an unrelated sharpening operation is performed on each pixel and then the results of the smoothing and sharpening operations are mixed using a soft-decision function. However, this technique increases the computational complexity of the image enhancement process even more, since now both the smoothing algorithm and the unrelated sharpening algorithm needs to be applied at each pixel.
A simpler method for combining smoothing and sharpening is based on linear unsharp masking, (Eq. 1) by modifying the local “sharpness gain factor” λ(ij) such that it has positive values (sharpening) in activity regions but negative values (smoothing) in flat regions. The local sharpness gain factor λ(ij) is in fact a soft-decision factor corresponding to a measure of the desired feature (activity). The computational complexity of this method is still relatively high since at each pixel both the high-pass filter response (H*x) and the activity measure λ(ij) must be determined. Also, neither the linear high-pass filter nor the activity measure differentiate between dither patterns and directional edges. It is hard to extend this method to handle different activity patterns in different ways, since both the high-pass filter and the activity measure must be redesigned.
Hence, what is needed is a simple manner in which to design efficient selective image sharpening or selective image sharpening and selective image smoothing filters.